Checkerboard puzzles of many types have been demonstrated in the past, the inventors being of the view that the main reference giving details of checkerboard puzzles is the “Compendium of Checker Board Puzzles” by Jerry Slocum and Jacques Haubrich published August 1993. Many puzzles may be constructed using the theory of combinatorial geometry upon which the puzzles shown in this Compendium are based. However, no relationship had been established between the obverse side and the reverse side of such puzzles until the '388 patent emerged in which a puzzle was taught having a plurality of polyomino pieces, each of which has on opposite sides one or more squares, the squares on each piece having markings such that the pieces are capable of being assembled using their obverse sides only into a first set of one or more solutions comprising a square checkerboard pattern with the markings of the squares on the obverse side, and wherein the pieces may be further assembled into a second set of one or more solutions comprising a further checkerboard pattern of two alternate markings, the markings on both sides of the pieces comprising three or more different markings and wherein the solutions of the first set are different from the solutions of the second set.
The '388 patent also provided a description of how this principle could be carried further to three-dimensional puzzles, in particular, a cube having, of course, square sides, but each side having a checkerboard pattern such that two opposite sides have the same features of the two sided puzzles of that invention, and pieces being so marked that the sides of the cube when assembled may have a checkerboard pattern comprising the markings carried by the obverse and reverse sides.
However, using the system proposed in the '388 patent, it is not possible to produce some particular checkerboard patterns using only two alternating colours per side to get, for example, diagonal stripes, particularly as applied to twelve pentomino plus one tetromino checkerboards. Where letters, numbers or other symbols having linguistic properties are provided in the place of coloured markings, there is no teaching of a paradigm for the production of particular non-exclusive solutions having a comprehensible statement or message.
It is an object of the present invention to provide advanced games and puzzles which alleviate one or more of the shortcomings of prior art. Other objects and advantages of the invention may become apparent from the following description.